A Two-Stage Stochastic Programming Model for Car-Sharing Problem using Kernel Density Estimation

Abstract: Car-sharing problem is a popular research field in sharing economy. In this paper, we investigate the car-sharing re-balancing problem under uncertain demands. An innovative framework that integrates a non-parametric approach - kernel density estimation (KDE) and a two-stage stochastic programming (SP) model are proposed. Specifically, the probability distributions are derived from New York taxi trip data sets by KDE, which is used as the input uncertain parameters for SP. Additionally, the car-sharing problem is formulated as a two-stage SP model which aims to maximize the overall profit. Meanwhile, a Monte Carlo method called sample average approximation (SAA) and Benders decomposition algorithm is introduced to solve the large-scale optimization model. Finally, the experimental validations show that the proposed framework outperforms the existing works in terms of outcomes.